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Welding, Bonding, and the Design of Permanent Joints 487
9–4 Stresses in Welded Joints in Bending

Figure 9–17a shows a cantilever welded to a support by fillet welds at top and bot-
tom. A free-body diagram of the beam would show a shear-force reaction V and
a moment reaction M. The shear force produces a primary shear in the welds of
magnitude

V
(a)
τ =
A
where A is the total throat area.
The moment M induces a horizontal shear stress component in the welds. Treating
the two welds of Fig. 9–17b as lines we find the unit second moment of area to be

bd 2
I u = (b)
2
The second moment of area I, based on weld throat area, is
bd 2
I = 0.707hI u = 0.707h (c)
2
The nominal throat shear stress is now found to be
Mc Md/2 1.414M
(d)
τ = = =
2
I 0.707hbd /2 bdh
The model gives the coefficient of 1.414, in contrast to the predictions of Sec. 9–2 of
1.197 from distortion energy, or 1.207 from maximum shear. The conservatism of the
model’s 1.414 is not that it is simply larger than either 1.196 or 1.207, but the tests
carried out to validate the model show that it is large enough.
The second moment of area in Eq. (d) is based on the distance d between the two
welds. If this moment is found by treating the two welds as having rectangular foot-
prints, the distance between the weld throat centroids is approximately (d + h). This
would produce a slightly larger second moment of area, and result in a smaller level
of stress. This method of treating welds as a line does not interfere with the conser-
vatism of the model. It also makes Table 9–2 possible with all the conveniences that
ensue.
The vertical (primary) shear of Eq. (a) and the horizontal (secondary) shear of
Eq. (d) are then combined as vectors to give

2 2 1/2
τ = (τ + τ ) (e)

Figure 9–17 y F
y
A rectangular cross-section h b
cantilever welded to a support b h
at the top and bottom edges.
x d z d
h

(a) (b) Weld pattern